10L 3s

This is the chromatic scale of the Sephiroth temperament explicated on the page for 3L 7s. However, a tempered-flat chain of the 13th harmonic really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered is descending order so that the the tempered 13th harmonic is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.

(Circle of fifths)	(ascending scale)
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X	L L L L s L L L s L L L s	Mode Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI	L L L s L L L s L L L s L	Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II	L L s L L L s L L L s L L	Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI	L s L L L s L L L s L L L	Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII	s L L L s L L L s L L L L	Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III	L L L s L L L s L L L L s	Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII	L L s L L L s L L L L s L	Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII	L s L L L s L L L L s L L	Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV	s L L L s L L L L s L L L	Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII	L L L s L L L L s L L L s	Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX	L L s L L L L s L L L s L	Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V	L s L L L L s L L L s L L	Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I	s L L L L s L L L s L L L	Elul

3/10		360
16/53		362.264
13/43		362.791
		363.487
10/33		363.818
		363.976
	27/89	364.045
		364.112
	17/56	364.286
7/23		365.217
		365.904
	18/59	366.102
		366.256
	29/95	366.316
		366.414
11/36		366.667
15/49		367.347
19/62		367.742
4/13		369.231